Solve the given initial-value problem: d²x/dt² + 9x = 4sin(3t), x(0) = 6, x'(0) = 0.
a) x(t) = 2sin(3t) + 6cos(3t)
b) x(t) = 4sin(3t) + 2cos(3t)
c) x(t) = 6sin(3t) + 4cos(3t)
d) x(t) = 8sin(3t) + 3cos(3t)